On irreducible elements of numerical semigroup algebras

Abstract

Given a numerical semigroup Sand a field F, the numerical semigroup algebra F[S] is a subalgebra of F[x] generated by monomials xs for s is an element of S. For a finite field Fq, we study distributions of irreducible elements of Fq[S]. We calculate the maximum number k of irreducible factors when an irreducible element of Fq[S] is factored in Fq[x]. We also show that the density of irreducible elements of degree n in Fq[S] has an asymptotic growth of (log n)k-1/n. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.